Question

梯形题目如图,梯形abcd的面积是12,ab=2cd,E是ac中点,be的延长线与ad交于f,△aef的面积,答案是4/

Answer 1

过E做EG//AB交AD于G

设梯形高为h

S梯形ABCD = (AB+CD)h/2 = 3CDh/2 = 12

∴CD×h = 8

S△ABC = AB×h/2 = CDh=8

∵E是AC的中点

∴S△AEB = S△ACB/2 = 4

∵E是AC的中点,GE//AB

∴G是AD的中点

∴GE = CD/2 = AB/4

∴EF：EB = GE：AB = 1：4

∴EF：EB = 1：3

∴S△AEF：S△AEB = 1：3

∴S△AEF = 4/3